Isotopic Equivalence from Bezier Curve Subdivision

We prove that the control polygon of a Bezier curve B becomes homeomorphic and ambient isotopic to B via subdivision, and we provide closed-form formulas to compute the number of iterations to ensure these topological characteristics. We first show that the exterior angles of control polygons converge exponentially to zero under subdivision.Comment: arXiv admin note: substantial text overlap with arXiv:1211.035

Enhanced collectivity in neutron-deficient Sn isotopes in energy functional based collective Hamiltonian

The low-lying collective states in Sn isotopes are studied by a five-dimensional collective Hamiltonian with parameters determined from the triaxial relativistic mean-field calculations using the PC-PK1 energy density functional. The systematics for both the excitation energies of $2^+_1$ states and $B(E2;0^+_1\to 2^+_1)$ values are reproduced rather well, in particular, the enhanced E2 transitions in the neutron-deficient Sn isotopes with N<66. We show that the gradual degeneracy of neutron levels 1g7/2 and 2d5/2 around the Fermi surface leads to the increase of level density and consequently the enhanced paring correlations from N=66 to 58. It provokes a large quadrupole shape fluctuation around the spherical shape, and leads to an enhanced collectivity in the isotopes around N=58.Comment: 5 pages, 4 figures, accepted for publication in Physics Letters

Covariant description of shape evolution and shape coexistence in neutron-rich nuclei at N\approx60

The shape evolution and shape coexistence phenomena in neutron-rich nuclei at $N\approx60$, including Kr, Sr, Zr, and Mo isotopes, are studied in the covariant density functional theory (DFT) with the new parameter set PC-PK1. Pairing correlations are treated using the BCS approximation with a separable pairing force. Sharp rising in the charge radii of Sr and Zr isotopes at N=60 is observed and shown to be related to the rapid changing in nuclear shapes. The shape evolution is moderate in neighboring Kr and Mo isotopes. Similar as the results of previous Hartree-Fock-Bogogliubov (HFB) calculations with the Gogny force, triaxiality is observed in Mo isotopes and shown to be essential to reproduce quantitatively the corresponding charge radii. In addition, the coexistence of prolate and oblate shapes is found in both $^{98}$Sr and $^{100}$Zr. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi surfaces of neutron and proton respectively. Furthermore, the 5-dimensional (5D) collective Hamiltonian determined by the calculations of the PC-PK1 energy functional is solved for $^{98}$Sr and $^{100}$Zr. The resultant excitation energy of $0^+_2$ state and E0 transition strength $\rho^2(E0;0^+_2\rightarrow0^+_1)$ are in rather good agreement with the data. It is found that the lower barrier height separating the two competing minima along the $\gamma$ deformation in $^{100}$Zr gives rise to the larger $\rho^2(E0;0^+_2\rightarrow0^+_1)$ than that in $^{98}$Sr.Comment: 1 table, 11 figures, 23 page

Mitigation of microbunching instability in x-ray free electron laser linacs

The microbunching instability seeded by small initial density modulation and driven by collective effects can cause significant electron beam quality degradation in next generation x-ray free electron lasers. A method exploiting longitudinal mixing derived from the natural transverse spread of the electron beam through a dispersive bending magnet was proposed to suppress this instability several years ago [Phys. Rev. Lett. 111, 054801 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.054801]. Instead of using bending magnets to introduce the transverse-to-longitudinal coupling, which will lead to an inconvenient deflection of the downstream beam line, in this paper, we propose a scheme to mitigate the microbunching instability by inserting a quadrupole magnet inside a bunch compressor of the accelerator. This results in transverse-to-longitudinal phase space mixing and large slice energy spread that can efficiently mitigate the growth of the microbunching instability through the major accelerator section. Finally, at the exit of the accelerator, a dogleg section is used to restore the emittance and slice energy spread before entering the undulator radiation section. Multiparticle simulations show that the transverse space charge, structure wakefield, and the coherent synchrotron radiation effects will have a relatively small impact on this scheme